What is (\partial)/(\partial a)((x)(ax^5+bx+3)) ?

The answer to (\partial)/(\partial a)((x)(ax^5+bx+3)) is x^6

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(\partial)/(\partial a)((x)(ax^5+bx+3))

\frac{\partial}{\partial a} ((x) (a x^{5} + b x + 3))

x^{6}

Solution steps

\frac{\partial}{\partial a} ((x) (a x^{5} + b x + 3))

Treat

x, b

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{\partial}{\partial a} (a x^{5} + b x + 3)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= x (\frac{\partial}{\partial a} (a x^{5}) + \frac{\partial}{\partial a} (b x) + \frac{\partial}{\partial a} (3))

\frac{\partial}{\partial a} (a x^{5}) = x^{5}

\frac{\partial}{\partial a} (b x) = 0

\frac{\partial}{\partial a} (3) = 0

= x (x^{5} + 0 + 0)

Simplify

x (x^{5} + 0 + 0) : x^{6}

= x^{6}

A (6, - 8) B (4, 2)

(e^{2 x} + 1)^{3}

\frac{5 x - 1}{( x + 1 ) ( x - 2 )}

- \frac{1}{2} (cos (x) + sin (x)) + C e^{x}

\frac{x ^{3} - 5 x ^{2} + 6 x + 2}{( x - 2 ) ^{2}}

What is (\partial)/(\partial a)((x)(ax^5+bx+3)) ?
The answer to (\partial)/(\partial a)((x)(ax^5+bx+3)) is x^6